Solve w=1/2(x+y-z)

$$w = \frac { 1 } { 2 } ( x + y - z )$$

Solve for x

$$x=2w+z-y$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+y-z.

$$w=\frac{1}{2}x+\frac{1}{2}y-\frac{1}{2}z$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}x+\frac{1}{2}y-\frac{1}{2}z=w$$

Subtract \frac{1}{2}y from both sides.

$$\frac{1}{2}x-\frac{1}{2}z=w-\frac{1}{2}y$$

Add \frac{1}{2}z to both sides.

$$\frac{1}{2}x=w-\frac{1}{2}y+\frac{1}{2}z$$

The equation is in standard form.

$$\frac{1}{2}x=\frac{z}{2}-\frac{y}{2}+w$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{\frac{z}{2}-\frac{y}{2}+w}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x=\frac{\frac{z}{2}-\frac{y}{2}+w}{\frac{1}{2}}$$

Divide w-\frac{y}{2}+\frac{z}{2} by \frac{1}{2} by multiplying w-\frac{y}{2}+\frac{z}{2} by the reciprocal of \frac{1}{2}.

$$x=2w+z-y$$

Solve for w

$$w=\frac{x+y-z}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x+y-z.

$$w=\frac{1}{2}x+\frac{1}{2}y-\frac{1}{2}z$$